Some Results On Quasiregular Coherent Configurations

In this paper,we introduced what are quasiregular coherent configurations and systems of linked quotients.Then we prove that they are equivalent.As for coherent configurations,the following results are obtained:For any coherent configuration X=(Ω，S),△is a subset of Ω,△(?)Ω,△ andΓ any fiber of X satisfy|△∩Γ|=1we define F:=F(X)is the set contains all △.·Let X be a quasiregular coherent configuration.Suppose that for any φ∈Isoalg(X,X’),any two distinct points α,β∈△∈F,and any α’,β’∈Ω’with φ(r(α,β))＝ r(α’,β’),there exists an injection f:△→Ω\such that(α,β)f=(α’,β’)and thatΥ(δ,γ)φ=Υ(δf,Υf),δ.Υ∈△Then X is separable and schurian.·A quasiregular coherent configuration with at most three fibers is schurian and separable.·Let(?)be a family of groups with distributive lattices of normal subgroup-s.Then any quasiregular coherent configuration of type(?)is schurian and separable.